Finite Group Databasebeta

← #14655543

Subgroups — #14655543

Order 2816.

528 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079767C211yesmaximal, characteristic, complemented
2#13078991C211yesmaximal, characteristic
3C2×#10622701C211yesmaximal, characteristic
4#13067285C211yesmaximal, characteristic
5#13067070C211yesmaximal, characteristic, complemented
6#13066454C211yesmaximal, characteristic, complemented
7C11×#1997C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#66927C2211yescharacteristic
10#10623001C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C4×C11×M16C2211yescharacteristic
13#10622744—22no—
14#10622706—21no—
15#10622704—22no—
16#10622701—22no—
17#10622701—22no—
18#10622691—21no—
19#10622583—22no—
20C2×#66873—22no—
21#10622538C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23#10622326—22no—
24#10622307—21no—
25#10622307—21no—
26C11×#343—22no—
27#10622123—22no—
28#10622122—22no—
29C22×Q8×C11—21no—
30C22×D44—21no—
31C22×D44—21no—
32C22×D44—21no—
33C2×C11×M16—21no—
34C2×C11×M16D412yes—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4D412yes—
41C2×C42×C11C2311yescharacteristic
42#66979—21no—
43#66977—21no—
44#66977—21no—
45C22×C11⋊C8—21no—
46#66927—21no—
47#66927—21no—
48#66927—21no—
49#66927D412yes—
50#66923—21no—
51#66922D411yescharacteristic
52#66922D411yescharacteristic
53C4×Dic22—21no—
54C4×Dic22—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×#97—21no—
58C4×C8×C11—21no—
59C22⋊(C11⋊C8)—21no—
60#66885—24no—
61#66885—24no—
62#66874—24no—
63#66873—28no—
64#66871—24no—
65C4⋊(C11⋊C8)D412yes—
66C4×C11⋊C8—21no—
67C4×C11⋊C8—21no—
68C4×C11⋊C8D412yes—
69#10149—111nomaximal, Sylow
70C23×D11—41no—
71C2×Q8×C11—41no—
72C2×Q8×C11—41no—
73C2×Q8×C11—82no—
74C22×C4×C11—22no—
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C2×D44—22no—
79C2×D44—22no—
80C2×D44—22no—
81C2×D44—44no—
82C2×D44—41no—
83C2×D44—41no—
84C2×D44—41no—
85C2×D44—42no—
86C2×D44—42no—
87C2×D44—82no—
88C2×Dic22—21no—
89C2×Dic22—21no—
90C11×M16—22no—
91C11×M16—22no—
92C11×M16—42no—
93C2×C8×C11—22no—
94C2×C8×C11—41no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103C22⋊Dic11—41no—
104C4⋊Dic11—21no—
105C4⋊Dic11—21no—
106C4⋊Dic11—21no—
107C4⋊Dic11—21no—
108Dic11⋊C4—41no—
109Dic11⋊C4—41no—
110C4×Dic11—41no—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—42no—
114#3230—111no—
115#3138—111no—
116C2×#486—111no—
117#1997D1111yescharacteristic, complemented
118#1545—111no—
119#1493—111no—
120#1278—111no—
121C23×C11#12111yescharacteristic
122C22×D11—42no—
123C22×D11—82no—
124C22×D11—82no—
125C22×D11—82no—
126Q8×C11—82no—
127Q8×C11—82no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—42no—
131C2×C4×C11—82no—
132C2×C4×C11#12011yescharacteristic
133C2×C4×C11#12011yescharacteristic
134C2×C4×C11#12011yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12111yescharacteristic
137C2×C4×C11#12711yescharacteristic
138C2×C4×C11#13512yes—
139C2×C4×C11#13712yes—
140C2×Dic11—41no—
141C2×Dic11—41no—
142D44—44no—
143D44—44no—
144D44—82no—
145D44—82no—
146D44—82no—
147D44—81no—
148D44—81no—
149Dic22—42no—
150Dic22—42no—
151C8×C11—42no—
152C8×C11—81no—
153C11⋊C8—42no—
154C11⋊C8—42no—
155#533—111no—
156C2×C4⋊Q8C2×D1111yescharacteristic
157C2×#127—111no—
158#500—221no—
159#490—222no—
160#487—221no—
161#486—221no—
162#486—221no—
163#486—222no—
164#486—222no—
165#484—222no—
166#477—222no—
167#431—111no—
168#423C2×D1111yescharacteristic
169#418—222no—
170C2×#102—222no—
171C4×M16C2×D1111yescharacteristic
172C2×C4×C8—111no—
173#343—22no—
174#331—222no—
175Q8⋊C8—222no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11#39211yescharacteristic
179C22×C11#46412yes—
180C2×D11—82no—
181C2×D11—82no—
182C2×D11—82no—
183C2×D11—164no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—82no—
187C4×C11#45212yes—
188C4×C11#45412yes—
189C4×C11#47212yes—
190C4×C11#49511yescharacteristic
191C4×C11#49711yescharacteristic
192Dic11—81no—
193Dic11—81no—
194C22×Q8—21no—
195C22×D4—221no—
196C22×D4—221no—
197C22×D4—221no—
198C2×M16—21no—
199C2×M16C22⋊D1112yes—
200C22×C8—221no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—111no—
206C4⋊Q8—111no—
207#127—112no—
208#127—221no—
209#127—221no—
210#127—221no—
211#125—221no—
212C22⋊Q8—221no—
213C22⋊Q8—221no—
214C4×Q8—221no—
215C4×Q8—221no—
216#117—221no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4D4412yes—
219C2×C42C22×D1111yescharacteristic
220#107—224no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—112no—
224#103—224no—
225#102—228no—
226#102—224no—
227#102—224no—
228C22⋊C8—221no—
229#97—21no—
230C4×C8—21no—
231C4×C8—112no—
232C4×C8—221no—
233C4×C8—221no—
234C2×C11—22no—
235C2×C11#200311yescharacteristic
236C2×C11#201511yescharacteristic
237C2×C11#201811yescharacteristic
238D11—162no—
239C24—441no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—82no—
243C2×Q8—221no—
244C2×Q8—221no—
245C2×D4—222no—
246C2×D4—222no—
247C2×D4—222no—
248C2×D4—444no—
249C2×D4—441no—
250C2×D4—441no—
251C2×D4—441no—
252C2×D4—442no—
253C2×D4—442no—
254C2×D4—882no—
255C22×C4—22no—
256C22×C4C2×D4411yescharacteristic
257C22×C4#433911yescharacteristic
258C22×C4C2×C22⋊D1111yescharacteristic
259M16—22no—
260M16—22no—
261M16—42no—
262C2×C8—22no—
263C2×C8—41no—
264C2×C8—222no—
265C2×C8—222no—
266C2×C8—442no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4—221no—
274C4⋊C4—221no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C22⋊C4—441no—
278C42—441no—
279C42D4×D1111yescharacteristic
280C42D4×D1111yescharacteristic
281C42D4×D1111yescharacteristic
282C42D4×D1111yescharacteristic
283C11#1014911yescharacteristic, complemented, Sylow
284C23—442no—
285C23—882no—
286C23—882no—
287C23—882no—
288C23#6698311yescharacteristic
289Q8—82no—
290Q8—82no—
291Q8—442no—
292Q8—442no—
293D4—444no—
294D4—444no—
295D4—882no—
296D4—882no—
297D4—882no—
298D4—881no—
299D4—881no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—42no—
303C2×C4—82no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4#6693511yescharacteristic
307C2×C4#6693511yescharacteristic
308C2×C4#6693711yescharacteristic
309C2×C4#6693711yescharacteristic
310C2×C4#6699011yescharacteristic
311C2×C4#6699311yescharacteristic
312C2×C4#6699512yes—
313C2×C4#6700312yes—
314C8—42no—
315C8—81no—
316C8—442no—
317C8—442no—
318C22—21no—
319C22—21no—
320C22—882no—
321C22—882no—
322C22—882no—
323C22—1764no—
324C22#1062257311yescharacteristic
325C22#1062264112yes—
326C4—21no—
327C4—21no—
328C4—82no—
329C4—881no—
330C4—881no—
331C4#1062236212yes—
332C4#1062236612yes—
333C4#1062266012yes—
334C4#1062267211yescharacteristic
335C4#1062269911yescharacteristic
336C2—22no—
337C2—1762no—
338C2#1306964011yescharacteristic
339C2#1306970911yescharacteristic
340C2#1306972411yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1997C2
socleC22×C11#392
prime radicalC2×#66927C22
hypercenter#1997D11
hypocenterC11#10149
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1997

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13079767C2semidirect
5. #13067070C2semidirect
6. #13066454C2semidirect
7. C11×#1997C2semidirect
117. #1997D11semidirect
283. C11#10149semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130797672
#130789912
C2×#106227012
#130672852
#130670702
#130664542
C11×#19972
#1014911